Population extremal optimisation for discrete multi-objective optimisation problems

The power to solve intractable optimisation problems is often found through population based evolutionary methods. These include, but are not limited to, genetic algorithms, particle swarm optimisation, differential evolution and ant colony optimisation. While showing much promise as an effective optimiser, extremal optimisation uses only a single solution in its canonical form – and there are no standard population mechanics. In this paper, two population models for extremal optimisation are proposed and applied to a multi-objective version of the generalised assignment problem. These models use novel intervention/interaction strategies as well as collective memory in order to allow individual population members to work together. Additionally, a general non-dominated local search algorithm is developed and tested. Overall, the results show that improved attainment surfaces can be produced using population based interactions over not using them. The new EO approach is also shown to be highly competitive with an implementation of NSGA-II.No Full Tex

Improved Multi-Population Differential Evolution for Large-Scale Global Optimization

Differential evolution (DE) is an efficient population-based search algorithm with good robustness, however, it is challenged to deal with high-dimensional problems. In this paper, we propose an improved multi-population differential evolution with best-and-current mutation strategy (mDE-bcM). The population is divided into three subpopulations based on the fitness values, each of subpopulations uses different mutation strategy. After crossover, mutation and selection, all subpopulations are updated based on the new fitness values of their individuals. An improved mutation strategy is proposed, which uses a new approach to generate base vector that is composed of the best individual and current individual. The performance of mDE-bcM is evaluated on a set of 19 large-scale continuous optimization problems, a comparative study is carried out with other state-of-the-art optimization techniques. The results show that mDE-bcM has a competitive performance compared to the contestant algorithms and better efficiency for large-scale optimization problems

A simple strategy for maintaining diversity and reducing crowding in differential evolution

Differential evolution (DE) is a widely-effective population-based continuous optimiser that requires convergence to automatically scale its moves. However, once its population has begun to converge its ability to conduct global search is diminished, as the difference vectors used to generate new solutions are derived from the current population members' positions. In multi-modal search spaces DE may converge too rapidly, i.e., before adequately exploring the search space to identify the best region(s) in which to conduct its finer-grained search. Traditional crowding or niching techniques can be computationally costly or fail to compare new solutions with the most appropriate existing population member. This paper proposes a simple intervention strategy that compares each new solution with the population member it is most likely to be near, and prevents those moves that are below a threshold that decreases over the algorithm's run, allowing the algorithm to ultimately converge. Comparisons with a standard DE algorithm on a number of multi-modal problems indicate that the proposed technique can achieve real and sizable improvements.IEEE Computational Intelligence Societ

MOMCMC: An Efficient Monte Carlo Method for Multi-Objective Sampling Over Real Parameter Space

In this paper, we present a new population-based Monte Carlo method, so-called MOMCMC (Multi-Objective Markov Chain Monte Carlo). for sampling in the presence of multiple objective functions in real parameter space. The MOMCMC method is designed to address the multi-objective sampling problem, which is not only of interest in exploring diversified solutions at the Pareto optimal front in the function space of multiple objective functions, but also those near the front. MOMCMC integrates Differential Evolution (DE) style crossover into Markov Chain Monte Carlo (MCMC) to adaptively propose new solutions from the current population. The significance of dominance is taken into consideration in MOMCMC\u27s fitness assignment scheme while balancing the solution\u27s optimality and diversity. Moreover, the acceptance rate in MOMCMC is used to control the sampling bandwidth of the solutions near the Pareto optimal front. As a result, the computational results of MOMCMC with the high-dimensional ZDT benchmark functions demonstrate its efficiency in obtaining solution samples at or near the Pareto optimal front. Compared to MOSCEM (Multiobjective Shuffled Complex Evolution Metropolis), an existing Monte Carlo sampling method for multi-objective optimization, MOMCMC exhibits significantly faster convergence to the Pareto optimal front. Furthermore, with small population size, MOMCMC also shows effectiveness in sampling complicated multiobjective function space

SQG-Differential Evolution for difficult optimization problems under a tight function evaluation budget

In the context of industrial engineering, it is important to integrate efficient computational optimization methods in the product development process. Some of the most challenging simulation-based engineering design optimization problems are characterized by: a large number of design variables, the absence of analytical gradients, highly non-linear objectives and a limited function evaluation budget. Although a huge variety of different optimization algorithms is available, the development and selection of efficient algorithms for problems with these industrial relevant characteristics, remains a challenge. In this communication, a hybrid variant of Differential Evolution (DE) is introduced which combines aspects of Stochastic Quasi-Gradient (SQG) methods within the framework of DE, in order to improve optimization efficiency on problems with the previously mentioned characteristics. The performance of the resulting derivative-free algorithm is compared with other state-of-the-art DE variants on 25 commonly used benchmark functions, under tight function evaluation budget constraints of 1000 evaluations. The experimental results indicate that the new algorithm performs excellent on the 'difficult' (high dimensional, multi-modal, inseparable) test functions. The operations used in the proposed mutation scheme, are computationally inexpensive, and can be easily implemented in existing differential evolution variants or other population-based optimization algorithms by a few lines of program code as an non-invasive optional setting. Besides the applicability of the presented algorithm by itself, the described concepts can serve as a useful and interesting addition to the algorithmic operators in the frameworks of heuristics and evolutionary optimization and computing

The 12 μm ISO-ESO-Sculptor and 24 μm Spitzer faint counts reveal a population of ULIRGs as dusty massive ellipticals: Evolution by types and cosmic star formation

Context. Multi-wavelength galaxy number counts provide clues to the nature of galaxy evolution. The interpretation per galaxy type of the mid-IR faint counts obtained with ISO and Spitzer, consistent with the analysis of deep UV-optical-near IR galaxy counts, provide new constraints on the dust and stellar emission. Discovering the nature of new populations, such as high redshift ultra-luminous (≥10^(12) L_⊙) infrared galaxies (ULIRGs), is also crucial for understanding galaxy evolution at high redshifts. Aims. We first present the faint galaxy counts at 12 μm from the catalogue of the ISO-ESO-Sculptor Survey (ISO-ESS) published in a companion article (Seymour et al. 2007a, A&A, 475, 791). They go down to 0.31 mJy after corrections for incompleteness. We verify the consistency with the existing ISO number counts at 15 μm. Then we analyse the 12 μm (ISO-ESS) and the 24 μm (Spitzer) faint counts, to constrain the nature of ULIRGs, the cosmic star formation history and time scales for mass buildup. Methods. We show that the “normal” scenarios in our evolutionary code PÉGASE, which had previously fitted the deep UV-opticalnear IR counts, are unsuccessful at 12 μm and 24 μm. We thus propose a new ULIRG scenario adjusted to the observed cumulative and differential 12 μm and 24 μm counts and based on observed 12 μm and 25 μm IRAS luminosity functions and evolutionary optical/mid-IR colours from PÉGASE. Results. We succeed in simultaneously modelling the typical excess observed at 12 μm, 15 μm (ISO), and 24 μm (Spitzer) in the cumulative and differential counts by only changing 9% of normal galaxies (1/3 of the ellipticals) into ultra-bright dusty galaxies evolving as ellipticals, and interpreted as distant ULIRGs. These objects present similarities with the population of radio-galaxy hosts at high redshift. No number density evolution is included in our models even if minor starbursts due to galaxy interactions remain compatible with our results. Conclusions. Higher spectral and spatial resolution in the mid-IR, together with submillimeter observations using the future Herschel observatory, will be useful to confirm these results

The 12 μm ISO-ESO-Sculptor and 24 μm Spitzer faint counts reveal a population of ULIRGs as dusty massive ellipticals: Evolution by types and cosmic star formation

Context. Multi-wavelength galaxy number counts provide clues to the nature of galaxy evolution. The interpretation per galaxy type of the mid-IR faint counts obtained with ISO and Spitzer, consistent with the analysis of deep UV-optical-near IR galaxy counts, provide new constraints on the dust and stellar emission. Discovering the nature of new populations, such as high redshift ultra-luminous (≥10^(12) L_⊙) infrared galaxies (ULIRGs), is also crucial for understanding galaxy evolution at high redshifts. Aims. We first present the faint galaxy counts at 12 μm from the catalogue of the ISO-ESO-Sculptor Survey (ISO-ESS) published in a companion article (Seymour et al. 2007a, A&A, 475, 791). They go down to 0.31 mJy after corrections for incompleteness. We verify the consistency with the existing ISO number counts at 15 μm. Then we analyse the 12 μm (ISO-ESS) and the 24 μm (Spitzer) faint counts, to constrain the nature of ULIRGs, the cosmic star formation history and time scales for mass buildup. Methods. We show that the “normal” scenarios in our evolutionary code PÉGASE, which had previously fitted the deep UV-opticalnear IR counts, are unsuccessful at 12 μm and 24 μm. We thus propose a new ULIRG scenario adjusted to the observed cumulative and differential 12 μm and 24 μm counts and based on observed 12 μm and 25 μm IRAS luminosity functions and evolutionary optical/mid-IR colours from PÉGASE. Results. We succeed in simultaneously modelling the typical excess observed at 12 μm, 15 μm (ISO), and 24 μm (Spitzer) in the cumulative and differential counts by only changing 9% of normal galaxies (1/3 of the ellipticals) into ultra-bright dusty galaxies evolving as ellipticals, and interpreted as distant ULIRGs. These objects present similarities with the population of radio-galaxy hosts at high redshift. No number density evolution is included in our models even if minor starbursts due to galaxy interactions remain compatible with our results. Conclusions. Higher spectral and spatial resolution in the mid-IR, together with submillimeter observations using the future Herschel observatory, will be useful to confirm these results

Two enhancements for improving the convergence speed of a robust multi-objective coevolutionary algorithm.

We describe two enhancements that significantly improve the rapid convergence behavior of DECM02 - a previously proposed robust coevolutionary algorithm that integrates three different multi-objective space exploration paradigms: differential evolution, two-tier Pareto-based selection for survival and decomposition-based evolutionary guidance. The first enhancement is a refined active search adaptation mechanism that relies on run-time sub-population performance indicators to estimate the convergence stage and dynamically adjust and steer certain parts of the coevolutionary process in order to improve its overall efficiency. The second enhancement consists in a directional intensification operator that is applied in the early part of the run during the decomposition-based search phases. This operator creates new random local linear individuals based on the recent historically successful solution candidates of a given directional decomposition vector. As the two efficiency-related enhancements are complementary, our results show that the resulting coevolutionary algorithm is a highly competitive improvement of the baseline strategy when considering a comprehensive test set aggregated from 25 (standard) benchmark multi-objective optimization problems

Using competitive population evaluation in a differential evolution algorithm for dynamic environments

This paper proposes two adaptations to DynDE, a differential evolution-based algorithm for solving dynamic optimization problems. The first adapted algorithm, Competitive Population Evaluation (CPE), is a multi-population DE algorithm aimed at locating optima faster in the dynamic environment. This adaptation is based on allowing populations to compete for function evaluations based on their performance. The second adapted algorithm, Reinitialization Midpoint Check (RMC), is aimed at improving the technique used by DynDE to maintain populations on different peaks in the search space. A combination of the CPE and RMC adaptations is investigated. The new adaptations are empirically compared to DynDE using various problem sets. The empirical results show that the adaptations constitute an improvement over DynDE and compares favorably to other approaches in the literature. The general applicability of the adaptations is illustrated by incorporating the combination of CPE and RMC into another Differential Evolution-based algorithm, jDE, which is shown to yield improved results.http://www.elsevier.com/locate/ejo